Optimal time-decay estimates for an Oldroyd-B model with zero viscosity

In this work, we consider the Cauchy problem for a diffusive Oldroyd-B model in three dimensions. Some optimal time-decay rates of solutions are derived via analysis upper and lower estimates provided that initial data small absolute value Fourier transform velocity is bounded below away from zero low-frequency region. It worth noticing independent fluid viscosity or coefficient, which different phenomenon incompressible Navier-Stokes equations.